On a space of entire functions rapidly decreasing on Rn and its Fourier transform

A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivati...

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Main Author:	Musin Il’dar Kh.
Format:	Article
Language:	English
Published:	De Gruyter 2015-11-01
Series:	Concrete Operators
Subjects:	Gelfand-Shilov spaces Fourier transform entire functions convex functions
Online Access:	http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2015-0007/conop-2015-0007.xml?format=INT

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spelling	doaj-73f26885caf04fea9fea1f91134456862020-11-25T01:06:13ZengDe GruyterConcrete Operators2299-32822015-11-012110.1515/conop-2015-0007conop-2015-0007On a space of entire functions rapidly decreasing on Rn and its Fourier transformMusin Il’dar Kh.0Institute of Mathematics with Computer Centre of RAS, Chernyshevsky str., 112, Ufa, 450077, RussiaA space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2015-0007/conop-2015-0007.xml?format=INTGelfand-Shilov spaces Fourier transform entire functions convex functions
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Musin Il’dar Kh.
spellingShingle	Musin Il’dar Kh. On a space of entire functions rapidly decreasing on Rn and its Fourier transform Concrete Operators Gelfand-Shilov spaces Fourier transform entire functions convex functions
author_facet	Musin Il’dar Kh.
author_sort	Musin Il’dar Kh.
title	On a space of entire functions rapidly decreasing on Rn and its Fourier transform
title_short	On a space of entire functions rapidly decreasing on Rn and its Fourier transform
title_full	On a space of entire functions rapidly decreasing on Rn and its Fourier transform
title_fullStr	On a space of entire functions rapidly decreasing on Rn and its Fourier transform
title_full_unstemmed	On a space of entire functions rapidly decreasing on Rn and its Fourier transform
title_sort	on a space of entire functions rapidly decreasing on rn and its fourier transform
publisher	De Gruyter
series	Concrete Operators
issn	2299-3282
publishDate	2015-11-01
description	A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.
topic	Gelfand-Shilov spaces Fourier transform entire functions convex functions
url	http://www.degruyter.com/view/j/conop.2014.2.issue-1/conop-2015-0007/conop-2015-0007.xml?format=INT
work_keys_str_mv	AT musinildarkh onaspaceofentirefunctionsrapidlydecreasingonrnanditsfouriertransform
_version_	1725190760068808704

On a space of entire functions rapidly decreasing on Rn and its Fourier transform

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